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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Spring 2016 • Question 6

Question

Math 6610 • Analysis of Numerical Methods I Spring 2016 • Question 6

Linear Multistep Methods

Give the definition of linear multistep method (give formula).

a) State necessary and sufficient condition for linear multistep method to be consistent.

b) State root condition for linear multistep method.

c) Construct an example of a consistent but not stable linear multistep method. Justify your answer.

Raw LaTeX

{Linear Multistep Methods}

Give the definition of linear multistep method (give formula).

\textbf{a)} State necessary and sufficient condition for linear multistep method
to be consistent.

\textbf{b)} State root condition for linear multistep method.

\textbf{c)} Construct an example of a consistent but not stable linear multistep
method. Justify your answer.

Topic Tags

Consistency, Stability, and Convergence Linear Multistep Methods Linear Programming and Optimization Zero-Stability and Root Conditions